Three dimensional imaging

ABSTRACT

A method and apparatus for imaging a sample, the method comprising the steps of: a) irradiating a sample to be imaged with a beam of pulsed electromagnetic radiation with a plurality of frequencies in the range from 25 GHz to 100 THz; b) detecting radiation which is both transmitted through and reflected from the sample; and c) generating an image of the sample from radiation detected in step (b). The method and apparatus can be used to generate a three-dimensional image of the sample and/or a compositional image of the sample.

The present invention relates to the field of imaging samples withradiation in the infra-red (IR) and Terahertz frequency range. Morespecifically, the present invention relates to apparatus and methods forimaging samples in three dimensions using electromagnetic radiation inthe higher Gigahertz (GHz) and the Terahertz (THz) frequency ranges.However, in this type of imaging technology, all such radiation iscolloquially referred to as THz radiation, particularly that in therange from 25 GHz to 100 THz, more particularly that in the range of 50GHz to 84 THz, especially that in the range from 100 GHz to 50 THz.

Recently, there has been much interest in using THz radiation to look ata wide variety of samples using a range of methods. THz radiation hasbeen used for both imaging samples and obtaining spectra. Work byMittleman et al, IEEE Journal of Selected Topics in Quantum Electronics,Vol. 2, No. 3, September 1996, page 679 to 692 illustrates the use ofusing THz radiation to image various objects such as a flame, a leaf, amoulded piece of plastic and semiconductors.

THz radiation penetrates most dry, non metallic and non polar objectslike plastics, paper, cardboard and non polar organic substances.Therefore, THz radiation can be used instead of X-rays to look insideboxes, cases etc. THz has lower energy, non-ionising photons thanX-rays, hence, the health risks of using THz radiation are expected tobe vastly reduced compared to those using conventional X-rays.

There is considerable interest in both medical and non-medical fields inthe production of 3D images. For example, in dentistry the ability toproduce 3D images of a tooth would enable dentists to locate exactlywhere caries (tooth erosion) or other abnormalities occur in the tooth.Most of the conventional imaging modalities—X-Ray, MRI, etc.—arehandicapped by the fact that they can intrinsically only produce 2Dimages, with 3D images possible only by translating the patient or bodypart through the X-Ray beam or through the magnetic field in the case ofMRI.

The use of THz for imaging the internal structure of a flat object (afloppy disc) has been described in EP 0 864 857. Here, the inventorsmeasured reflection of a beam of THz radiation to produce an image ofthe internal structure of the sample.

However, this method is not suitable for obtaining 3D images of objectswhere the front and back surfaces are curved. Most objects haveinterfaces and/or external surfaces which are non-planar, i.e. havesubstantial radii of curvature. If a beam is reflected from a curvedsurface, it is reflected at an angle to the incident beam. The method ofEP 0 864 857 does not show how to obtain an image when the radiation isreflected from a curved surface.

Also, partially absorbing objects give rise to weak reflections fromburied layers resulting in long absorption lengths for certain reflectedpulses. This limits the thickness of objects which can be accuratelyimaged in 3D using THz reflection data alone.

The present invention addresses the above problems in a first aspectprovides a method of imaging a sample, the method comprising the stepsof:

(a) irradiating the sample to be imaged with an irradiating beam ofpulsed electro magnetic radiation with a plurality of frequencies in therange from 25 GHz to 100 THz,

(b) detecting both the radiation transmitted through the sample and theradiation reflected by the sample;

(c) generating an image of the sample from the radiation detected instep (b).

Collecting both the reflected and transmitted radiation allows a greaterrange of curved surfaces to be measured. Hence, the method of thepresent invention is capable of imaging a sample of virtually any shape.The collection of both the transmitted and reflected radiation alsoallows a compositional image of the sample to be obtained.

Radiation transmitted through the sample is primarily used to determinethe sample shape and the composition. Radiation which is reflected fromthe sample is primarily used to measure the positions of dielectricsurfaces within the sample in addition to giving shape information. Thistechnique allows the curvature of both internal and external surfaces tobe measured. Thus, using both reflected and transmitted radiation is anextremely powerful tool to determine the three dimensional compositionalstructure of the object.

Taking a uniform sphere as a simplified example. In such an examplethere are no internal interfaces. Therefore, the pulse is at eithertransmitted through the sphere or will be reflected on entering orexiting the sphere. Subdividing the sample into a 2D array of pixels andmeasuring the time of flight of the transmitted pulse through the samplewill allow the thickness of the sample to be determined at each pixel.However, this will not determine the shape of the sample as the positionand shape of the front interface is not known. The shape of the frontinterface can be determined from the time of flight of the pulse whichis reflected on entering the sphere. Thus, it is possible to obtaininformation about the shape of a sample by plotting the differencebetween the time of flight of the transmitted and reflected pulsesrelative to the time of flight of the reflected pulse.

Therefore, the step of generating the image preferably comprises thesteps of calculating the time of flight of the pulse transmitted throughthe sample; calculating the time of flight of a pulse reflected from aninterface or surface of the sample; and plotting the difference or afunction of the difference of the time of flight of the transmittedpulse and the reflected pulse relative to the time of flight of thereflected pulse.

A function of the difference can be plotted in order to correct forvariations in the refractive index of the sample.

In the case of a sphere, theoretically, the pulse reflected on exitingthe sphere could be used to determine the shape of the sample inconjunction with the pulse reflected on entering the sphere. However, itis not desirable to use the pulse reflected on exiting the sample as itwill be scattered through a fairly large angle, possibly outside therange of the detector. Further, as the reflected pulse has passed twicethrough the sample, it is likely to be very weak.

The present invention can be used to image far more complex objects thanthe above uniform sphere. As mentioned above, it is difficult to detecta reflected pulse from the interfaces which are deepest within thesample. Such a complex sample is measured using a reflected radiationdetector (or detectors) which is located at the same side on the sampleas the incident THz pulse and a transmitted radiation detector (ordetectors) which is located on substantially the opposite side of thesample to the incident THz pulse. In a sample with many interfaces, someof the radiation detected by the transmitted radiation detector willhave been transmitted through the whole of the sample. However, some ofthe radiation collected will have undergone multiple reflections. Forexample, radiation can be reflected back into the sphere from thesphere's external surface onto an internal interface. The pulse is thenreflected for a second time at the internal interface out of the sphere.This reflected pulse will be collected by the transmitted radiationdetector. The position of interfaces deep within the sample can bedetermined by looking at the signal due to such doubly reflected pulsesor pulses which have undergone an even number of reflections.

Therefore, preferably, the step of generating the image comprises thestep of extracting the parts of the detected transmitted pulse which aredue to an even number of reflections within the sample, and determiningthe position of an interface using the said signal caused by said evennumber of reflections.

In order to be able to directly compare the reflected and transmittedsignals, it is preferable if a reference signal is provided. Saidreference signal is preferably provided by a reflection off an objectwhich is a known distance with respect to either the source of THzradiation or the sample being imaged. The reflection may be taken froman object, which is preferably planar located between the source of theradiation and the sample being imaged and is preferably taken from areflection off a component of the source itself.

In addition to collecting both transmission and reflection data, it ispreferable if the resolution of the system is not limited by thediffraction limit. Therefore, it is preferable if the beam whichirradiates the sample has a beam diameter which is smaller than thesmallest wavelength of radiation in the pulse of electromagneticradiation.

To obtain an image of the whole sample, the sample is preferablysubdivided into a 2 dimensional pixel array. The radiation which iseither reflected by or transmitted through each pixel is detected. Theimage is then generated pixel by pixel.

Preferably, the sample which is to be imaged is placed on a motorisedstage, which can be stepped in the both the x and y directions. An imageof the entire sample can then be generated pixel by pixel.

Due to the beam diameter being smaller than the wavelength of theradiation, the present invention utilises near-field techniques. Hence,the spatial resolution is not determined by the focused spot size of theTHz beam.

The beam of pulsed radiation which is used to irradiate the sample ispreferably generated by an emitter which has non-linear opticalproperties. The material of the emitter is preferably chosen such thatwhen the emitter is irradiated with radiation with a predetermined inputfrequency or frequencies, the emitter emits a beam with the desiredoutput frequency or frequencies i.e. a frequency or frequencies in therange from 50 GHz to 84 THz. The frequency of the emitted beam isdetermined by both the frequency or frequencies of the input radiationand the non-linear properties of the emitter itself.

The emitter can be a semiconductor crystal with non-linear opticalproperties type which allow visible pulses of light (i.e. pulses withwavelengths in the range from 0.3 μm to 1.5 μm) to be converted topulses with a wavelength in the range from 50 GHz to 84 THz. The emittermay be chosen from a wide range of materials, for example, LilO₃,NH₄H₂PO₄, ADP, KH₂PO₄, KH₂ASO₄, Quartz, AlPO₄, ZnO, CdS, GaP, GaAs,BaTiO₃, LiTaO₃, LiNbO₃, Te, Se, ZnTe, ZnSe, Ba₂NaNb₅O₁₅, AgAsS₃,proustite, CdSe, CdGeAs₂, AgGaSe₂, AgSbS₃, ZnS, DAST(4-N-methylstilbazolium) or Si. Other types of emitter could be used,for example, photoconductive antennas which emit radiation in thedesired frequency range in response to irradiation by an input beamhaving a different frequency and upon the application of a bias to theantenna.

In the case of an emitter which has non-linear optical properties, tokeep the input beam in phase with the emitted beam (THz beam), theemitter preferably comprises phase matching means. The phase matchingmeans can be of the type for enhancing the phase matching between atleast two different frequency signals propagating in the emitter inresponse to illumination by at least one incident beam of radiation, thephase matching means having a spatial rotation in its refractive indexalong a component of the incident radiation beam.

Preferably, the diameter of the beam which irradiates the sample isdetermined by the diameter of the visible or near-infrared beam whichirradiates the emitter. In this situation, there is no need to haveextra active optical components between the sample and the emitter tofocus the beam. However, in such an arrangement, the sample needs to bepositioned close to the emitter. The sample may be mounted directly ontothe emitter. Alternatively, the sample may be mounted in very closeproximity to the semiconductor emitter. For example, between 10 and 500μm. Also, the sample may be mounted on a passive optical component whichis invisible to THz radiation i.e. a window. The window does not serveto focus the beam.

It may be preferable to separate the emitter and the sample, if theemitter comprises a toxic material, for example, ZnTe.

In the method of the present invention, both transmitted and reflectedradiation pulses are measured. When an emitter of the type describedabove is used, the reflected THz passes must pass back through theemitter (without significant losses) before they are collected asreflected THz for analysis. Therefore, preferably, the emitter istransparent to THz radiation or at least to the radiation of theirradiating beam. Semiconductors with a low carrier doping concentrationare useful for this aspect.

The present invention uses both transmission and reflection in order todetermine the internal and external shape of the sample. The need tomeasure, at the reflected signal detector, the pulse which has beenreflected once from the curved interfaces located deep within the sampleis avoided. However, the reflected signal will be measured from thecurved interfaces which are close to the front interfaces. In order topermit a range of sample sizes and radii of surface or interfacecurvatures which are close to the front of the sample to be measured,the emitter must also be sufficiently large to allow all of thereflected beams to pass back through the emitter. If the emitter is toosmall, or if the imaging takes place too close to the edge of theemitter, some of the reflections may be blocked by the mount of theemitter. To allow a smaller crystal to be used, it is preferable if justthe sample moves in order to image the area of the sample. As the samplemoves relative to both the emitter and the input beam of the emitter, asmaller emitter can be used.

To further reduce the size of the emitter, the emitter may be mounted ona “THz window”. The window material could be for example polyethylene,polythene, high-resistivity silicon, Z-quartz or TPX(poly-4-methylpentene-1), it must be at least substantially transparentto the irradiating beam. The window would preferably be thin, forexample, between 50 and 300 microns. This is to ensure that the THz beamdiameter is still smaller than the shortest wavelength component whenthe THz beam reaches the sample. The size of the window is large enoughto allow all of the reflected beams to be collected with negligibleloss. As the emitter is provided on the window which is substantiallytransparent to THz, the THz can pass through the mount for the emitter.

Also, using conventional coherent THz detection methods, for example,electro-optic sampling and photoconductive detection, the THz beam mustbe focused to a point and thus information is lost about the path thedifferent THz beams take following reflection. This problem can beaddressed by using a CCD camera. Therefore, it is preferable if a CCDcamera is used in the detection the reflected THz beams. This detectionmethod allows reflection techniques to map out the shape of curvedsurfaces, also, it would be possible to map out differences in shapebetween internal and external dielectric surfaces.

It should be noted that the CCD camera would probably not be used todetect the THz directly, instead the THz would be converted to a visibleor near IR radiation an electro-optical component, the near IR visibleradiation would then be collected by the CCD. Preferably, thisconversion to IR or visible radiation would be achieved by passing apolarised reference beam with the THz beam through a material whichsupports the AC pockets effect. The light emitted by the material isthen passed through a polariser to the CCD. Only light which has had itspolarisation rotated by the THz signal will be transmitted be thepolariser into CCD.

Also, when collecting the output light using an off axis parabolicmirror, there is a slight time delay due to the different optical pathlengths between the centre and the edge of the mirror. Consequently, thedifferent path lengths of the reflected beams cause the pulses to arriveat different times at the detector. This causes a problem, because it isnot easy (if at all possible) to distinguish between a time-shift of apulse due to the position of an internal dielectric layer and a timeshift which is a combination between a reflection from the sample and adifferent path length due to one of the optical mirrors. This problemcan also be addressed by the use of a CCD camera as a detector. A CCDcamera can be used to image a 2D region containing all the reflected THzbeams, both the temporal and spatial shift if the THz can be measured.In other words, more exact information about the sample can be gained byusing a CCD camera.

The CCD technique can be used to collect radiation which is bothtransmitted and reflected from the sample. As in many situations, thetransmitted beam may also be transmitted off axis.

In the method of the present invention, data can be derived by using thetime-of-flight method. As the enters the sample, its velocity changesdue to variations in the refractive index of the sample. Thus, bymeasuring the time of flight of the pulse through the sample, an imageof the sample shape can be obtained using transmission.

Using the frequency domain analysis techniques of UK application no9940166.7, the composition of the structure can be determined. In thisapplication, a single frequency from the plurality of transmitted orreflected plurality of frequencies is used to generate the image. Insome cases, a narrow range of frequencies or a selection of specificfrequencies or frequency ranges is studied. A selected frequency rangeis taken to be a frequency range typically less than a third of thetotal range of the passed electromagnetic radiation used to irradiatethe sample. More preferably, the selected frequency range is less than10% of the total frequency range of the passed electromagnetic radiationused to irradiate the sample.

For example, water is a strong absorber of THz radiation. There are“windows” in the water absorption spectra from 50 GHz to 500 GHz, from30 THz to 45 THz and from 57 THz to 84 THz. If the sample is irradiatedwith a range of frequencies from 50 GHz to 84 THz, it may be preferableto generate the image using one or more of the following selectedfrequency ranges: 50 GHz to 500 GHz, 30 THz to 45 THz and 57 THz to 84THz. The image may be generated by integrating over the selectedfrequency range.

Thus, by analysing the transmitted information as above, an image can becreated by a single frequency or a selected frequency range. Also, aplurality of images may be derived from a plurality of frequencies or asingle image may be derived from two or more distinct frequencies. Thisis a very powerful analysis and allows variations in the composition ofthe material to be determined.

The image or images may be generated in a number of ways. For example, asequence of images may be generated from a plurality of differentfrequencies.

In general, the present invention will be performed using imagingapparatus which is configured to detect temporal data at each pixel.Preferably, the data is Fourier transformed to give the complex THzelectric field in the frequency domain E (ω).

The image can be obtained in a number of ways from the complex THzelectric field E(ω), e.g.:

(i) The power spectrum P_(sample) (ω) of the sample and the powerspectrum P_(ref) (ω) of the reference signal may be calculated. Theimage could then be generated by plotting the difference between the twoPower spectrums for a given frequency for each pixel at a selectedfrequency over integrated over a selected frequency range.

(ii) The power spectrum P_(sample) of the sample and the reference powerspectrum P_(ref) may be divided to give the transmittance. Thetransmittance may then be plotted for each pixel at a selected frequencyover integrated over a selected frequency range.

(iii) The frequency dependent absorption coefficient α(ω) may becalculated from the complex electric field E(ω) and plotted for eachpixel at a selected frequency over integrated over a selected frequencyrange.

(iv) The frequency dependent refractive index η(ω) may also becalculated from the complex electric field and plotted for each pixel ata selected frequency over integrated over a selected frequency range.

The detected temporal electric field contains both phase and amplitudeinformation which give a complete description of the complex dielectricconstant of the medium in the beam path. The sample to be characterisedis inserted into the beam and the shape of the pulses that havepropagated through the sample or have been reflected from the sample arecompared with the reference temporal profile acquired without thesample. The ratio of the complex electric field E(ω) and the referencesignal E_(ref)(ω) is calculated to give the complex response function ofthe sample, S(ω). In the most simple case, the complex response functionis given by: $\begin{matrix}{{S(\omega)} = {\frac{E(\omega)}{E_{ref}(\omega)} \propto {{\exp \left( {\frac{i\quad \omega \quad d}{c}\left( {{\eta (\omega)} - 1} \right)} \right)}{\exp \left( {{- {\alpha (\omega)}}d} \right)}}}} & (1)\end{matrix}$

where d is the sample thickness, c is the velocity of light in vacuum, ηis the refractive index and α is the absorption coefficient. Theexperimental absorption coefficient α(ω) and the refractive index η(ω)may then be easily extracted from the magnitude M(ω) and the phase φ(ω)of S(ω), respectively, according to $\begin{matrix}{{\alpha (\omega)} = {{- \frac{1}{d}}{\ln \left( {M(\omega)} \right)}}} & (2) \\{{\eta (\omega)} = {1 + {\left( \frac{c}{\omega \quad d} \right){\varphi (\omega)}}}} & (3)\end{matrix}$

Additional terms may be included in equations (1) to (3) to account forreflections at dielectric interfaces of a sample, thus allowing accurateanalysis of multilayered samples.

These parameters are simply related to the complex dielectric function∈(ω) of the sample

 ∈(ω)=(η(ω)+ik(ω))²=(η(ω)+iα(ω)c/2ω)²  (4)

The data derived as discussed in (i) to (iv) above, may be directlyplotted either as a colour or a grey scale image where the colour orshade of grey of each pixel represents a given magnitude.

Instead of a single frequency, a selected frequency range could bechosen and the result and data of (i) to (iv) integrated over thatrange. The integrated data could then be plotted.

It may also be preferred to subdivide the magnitude of the data processin accordance with any of (i) to (iv) above into various bands. Forexample, all data below a certain value could be assigned the value 0,all data in the next magnitude range could be assigned the value 1, etc.These ranges may have equal widths in magnitude or they may havedifferent widths. Different widths may be preferable to enhance contraste.g. to emphasise contrast in regions of the sample where there islittle variation in the sample absorption of Thz.

Preferably, the present invention uses two or more frequencies. The datafrom say two frequencies is processed in accordance with any of (i) to(iv) above. The data is then banded as described for a single frequencyabove.

The data may be split into two hands, one assigned the value “0” and theother “1”. The data from both frequencies can then be added togetherusing a rule such as a Boolean algebraic expression e.g. AND, OR, NOT,NAND, XOR, etc.

Of course, the present invention also allows images to be compared fromtwo different frequencies. This may be particularly useful to identify asubstance where the absorption to THz changes over a certain frequencyrange.

Thus, complex images can be produced. This system is particularly usefulin the detection of breast cancer where both spatial information andcompositional information concerning the 3D structure of the breast canbe derived. Also, the present invention can be used to image teeth andbone.

The method of the present invention allows the internal composition,shape and the position of the internal surfaces to be determined. Hence,a three dimensional image of the sample can be produced from the methodsof the three aspects of the present invention. In a second aspect, thepresent invention provides an apparatus comprising:

a) means for irradiating a sample to be imaged with an irradiating beamof pulsed electromagnetic radiation with a plurality of frequencies inthe range from 25 GHz to 100 THz;

b) means for detecting radiation which is both transmitted through andreflected from the sample; and

c) means for generating an image of the sample from radiation detectedin step (b).

For the reasons described above, it is preferable if the imaging isperformed in the near-field regime. Therefore, it is preferable if themeans for radiating a sample comprises an emitter for emitting a beam ofradiation with a plurality of frequencies in the range from 25 GHz to100 THz, the emitter having optical non linear properties, such thatwhen the emitter is irradiated with an input beam with a frequency inthe visible or near infra-red frequency ranges, a beam is emitted withfrequencies in the range from 25 GHz to 100 THz. Preferably, the inputbeam of pulsed radiation has a diameter which is smaller than that ofthe smallest wavelength of the emitted beam.

To image the sample, the sample should be stepped pixel by pixel in twoorthogonal directions. Therefore, it is preferable that the apparatusfurther comprises a motorised stage configured so that it can be steppedpixel by pixel into two orthogonal directions.

The sample itself can be mounted on the motorised stage. Alternatively,both the sample and the emitter can be mounted on the motorised stage.

The present invention will now be described with reference to thefollowing preferred non-limiting embodiments, shown in the followingdrawings in which:

FIG. 1 shows a schematic near-field transmission and reflection imagingsystem according to an embodiment of the present invention;

FIG. 2 shows the system of FIG. 1 with a source and detectors for boththe transmitted and reflected radiation;

FIG. 3 shows a variation on the imaging system of FIG. 2;

FIG. 4 shows the imaging system of FIG. 2 with details of the detectors;

FIG. 5 shows the imaging system of FIG. 2 with details of the detectors;

FIG. 6 shows the imaging system of FIG. 2 with details of the detectors;

FIG. 7 shows a variation on the imaging system of FIG. 6;

FIG. 8 shows a variation on the imaging system of FIGS. 6 and 7.

FIGS. 9a, 9 b and 9 c show three variations on the method of mountingthe sample to be imaged;

FIG. 10 shows a schematic of a uniform sphere for explaining a method inaccordance with an embodiment of the present invention;

FIG. 11 shows a schematic of a sphere having a plurality of internalinterfaces for explaining a method in accordance with an embodiment ofthe present invention; and

FIG. 12 shows an embodiment of the present invention used for imaging atooth.

FIG. 1 is a schematic of a near-field transmission and reflectionimaging system. A focused visible beam (which has a wavelength in thevisible electro-magnetic region i.e. typically between 0.3 μm to 1.5 μm)1 is focused onto a THz emitter 3. The THz generation crystal is acrystal with non-linear properties which will emit radiation in the THzregime (50 GHz to 84 THz) when irradiated by visible light. The THzpulse 5, is emitted from the THz generation crystal 3. The actualfrequency of the emitted beam is determined by the frequency of theinput radiation and the physical properties of the emitter itself. Anemitted beam with the desired frequency range can be obtained byappropriate selection of the emitter material and the frequency of theinput radiation.

The diameter of the input which impinges on the THz generation crystal,is smaller than that of the smallest wavelength which will be generatedin the THz pulse from the emitter 3. The sample 7, is directly mountedonto the emitter 3. Therefore, the sample is imaged with a beam of THzradiation which has a beam diameter which is less than that of thesmallest wavelength of the THz light. Thus, the resolution of the imageobtained from the sample will not be limited by the diffraction limit.

Some of the THz pulse will be transmitted through the sample 7. Thetransmitted THz is denoted by reference numeral 9. THz pulses will alsobe reflected from the sample 10. In this specific example, the firstreflection of the THz pulse 5 occurs at the interface 11 between thesample 7 and the emitter 3. A second dielectric interface 13 within thesample 7 causes reflection R₂ which is the second reflected THz pulse.This pulse will be reflected at a time Δτ₁ the third reflection R₃occurs as the THz pulse leaves the sample 7. By collecting both thereflected and transmitted pulses, considerable detail about sample 7 canbe determined.

The reflected THz pulses 10 are collected by off axis parabolic mirror12. The passes are then reflected into a detector (not shown). The offaxis parabolic mirror 12 has a hole 14 for transmitting the focusedvisible beam 1 from the source (not shown) to the emitter 3.

FIG. 2 shows a complete system. For convenience, like numerals denotelike components on the previous and remaining figures. Pulse lasersource 21 provides the beam of visible light 1. The beam of light 1impinges on beam splitter 23. The beam splitter may be a half silveredmirror or the like. Beam splitter 23 passes a part of the visible pulse25 towards the emitter 3 and a second part of the visible pulse 27 isreflected towards the detection mechanism. This beam 27 will eventuallybe used as a reference beam in the detection mechanism. Initiallylooking at the visible beam 25 which is used for generating the THzbeam, this is first passed through an off axis parabolic mirror 29. Theoff axis parabolic mirror 29 has a hole to allow transmission of thevisible pulse therethrough. The pulse is then directed onto the emitter3 as shown in FIG. 1.

As explained above in relation to FIG. 1, the THz pulse 5 is reflectedoff the external surfaces and dielectric internal surfaces of the sample7. This reflected pulse 31 is then collected by off axis parabolicmirror 29 (this is the same mirror through which the visible pulse 25passes). The mirror 29 reflects the pulse into THz detector 33 which isused to produce the image. A second off axis parabolic mirror 35 is usedto collect the transmitted THz pulse 37 from the sample 7. The off axisparabolic mirror 35 directs the transmitted pulse onwards transmittedpulse THz detector 39.

Visible pulse 27 is directed via mirrors, 43, 45 and 47 into THzdetectors 33 and 39. An optical delay line 49 is provided to synchronisethe visible pulse 27 with the collected reflected and transmitted THzradiation. As the reflected and transmitted THz radiation passes throughthe sample, the pulse is delayed, the optical delay line compensates forthis effect.

FIG. 3 shows a variation of the imaging system of FIG. 2. FIG. 3, isvery similar to FIG. 2. However, here, the visible beam 25 impinges on adichoric beam splitter 51. The beam splitter is ideally 100% reflectiveto the visible light but 100% transparent to the reflected THz beam. Inthis arrangement, the dichoric mirror 51 reflects the beam onto the offaxis parabolic mirror 29. The off axis parabolic mirror then directs thevisible beam onto the emitter 3. As the visible beam 25 is beingreflected from the off axis parabolic mirror, the off axis parabolicmirror 29 can be used to focus the beam to a small diameter (about 100microns) on the generation crystal 3.

The reflected THz pulse 31 is collected in the same manner as describedfor FIGS. 1 and 2, the reflected pulse as collected by off axisparabolic mirror 29. The off axis parabolic mirror 29 directs thereflected pulse 31 onto dichoric mirror 51. The dichoric mirror istransparent to THz therefore it transmits the pulse 31 into THz detector33.

The collection of the transmitted radiation 37 and the direction of thereference beam 27 into detectors 33 and 39 is identical to thatdescribed in FIG. 2.

FIG. 4 shows a full detection system using electro-optical detection.The system is largely identical to that of FIG. 2. However here, the THzdetectors 33 and 39 are shown in more detail. Detection systems 33 and39 are identical. Therefore, for simplicity only detection system 33will be described.

In the detector 33 the THz beam carrying the reflected sampleinformation 101 and a visible light beam 27 are combined using an offaxis parabolic mirror 103. The off axis parabolic mirror 103 has a holefor the transmission of the visible beam 27 therethrough. Both thevisible beam 27 and the reflected beam 101 are then directed onto a THzdetection crystal 105. The visible light beam 27 acts as a referencebeam which is incident on the detection crystal 105. Each of the axeshas distinct refractive indices n_(o) and n_(e) along the ordinary andextraordinary axis of crystal 105 respectively. In the absence of asecond THz radiation beam 101, the linearly polarised reference beam 27passes through the detection crystal 105 with negligible change to itspolarisation.

The applicant wishes to clarify that although the angle through whichthe polarisation is rotated by is negligible, the linearly polarisedbeam can become slightly elliptical. This effect is compensated for by avariable retardation wave plate, e.g. a quarter wave plate 107. Theemitted beam is converted into circularly polarised light using thequarter wave plate 107. This is then split into two linearly polarisedbeam by a beam splitter such as a Wollaston prism 109 which directs thetwo orthogonal components of the polarised beam onto a balancedphotodiode assembly 111. The balanced photodiode signal is adjustedusing wave plate 107 such that the difference in outputs between the twodiodes is zero.

However, if the detector 107 also detects a secondary beam 101 (in thiscase a beam with a frequency in the THz range) as well as the referencebeam, the angle through which the polarisation is rotated is notnegligible. This is because the THz electric field modifies therefractive index of the visible (fundamental) radiation along one of theaxes n_(e), n_(o). This results in the visible field after the detector105 being elliptical and hence the polarisation component separated bythe prism 109 are not equal. The difference in the signal between thediode outputs gives a detection signal.

The reference beam 27 and the THz beam 101 should stay in phase as theypass through the crystal 105. Otherwise, the polarisation rotation isobscured. Therefore, the detection crystal 105 has phase matching meansto produce a clear signal.

The optical delay is introduced by cube mirror 121 and plane mirror 123.Cube mirror 121 moves in and out to vary the length of the optical pathand of the reference beam 27.

FIG. 5 shows a variation on the system of FIG. 4. Here, photoconductivedetection by photoconductive THz detectors 131 and 133 are used todetect the transmitted and reflected THz beam.

The system shown in FIGS. 4 and 5, the systems have a single opticaldelay line (which is achieved by cube mirror 121 and plane mirror) thatservices both detection elements. Alternatively, a separate delay linefor each detection element could be used. This may be necessary whenvery thick objects are imaged. Here, the transmitted THz pulse wouldexperience a longer delay than the pulse reflected from the frontsurface. Hence, a single optical delay may not be suitable.

The off axis parabolic mirrors 29, 35 need to be carefully aligned toensure efficient collection of both the transmitted 37 and reflected 31THz beams.

If a THz beam is incident on a curved surface, i.e. one with a surfacenormal not parallel to the direction of the THz beam, the THz beam willnot be reflected along the same axis. Instead, it will be reflected atan angle which increases with the surface curvature.

In the two above THz detection methods, the THz is focused to a pointfor detection, thus information about the path the different THz beamstake following reflection can be lost.

Also, when collecting the output using an off axis parabolic mirror,there is a slight time delay due to the different optical path lengthsbetween the centre and the fringe and the mirror. Consequently, thedifferent path lengths reflected beams would cause the pulses to arriveat different times at the detector. Using the detection methods of FIGS.4 and 5, the beams are focused to a single point. This causes a problemas it is difficult (if not impossible) to discriminate between a timeshift due to the opposition of dielectric layer and a time shift that isa combination of the dielectric position and a different paths length onthe mirror. The effects of different paths to the mirror are greatestwhen the surfaces/interfaces are sharply curved. However, if using a CCDcamera both the temporal and spatial shift of the THz beam can bemeasured and this allows the exact curvature of the sample pixel bypixel to be determined.

FIG. 6 shows a similar system to that of FIGS. 4 and 5. The differenceis that the detection mechanism of FIG. 6 uses a CCD.

The reference beam 27 is reflected off mirror 47 and is polarised bypassing the beam through polariser 142. The polarised reference beam 27is then combined with the reflected radiation 101 using beam splitter102. The beam splitter is transparent to THz radiation and hence THzradiation is transmitted through beam splitter 102. However, it is nottransparent to visible light and hence the reflected polarised referencebeam 27 is combined with the THz beam. The reflected THz beam 101 andthe reference beam 27 are directed toward detector crystal 141. Thisdetection mechanism is based on AC Pockles effect and the polarisationof reference beam 27 is rotated by the presence of reflected THz beam101. The emergent beam 139 is then passed through polariser 140.Polarisers 140 and 142 are crossed relative to each other. Therefore, ifno THz beam is present, the polarisation of beam 27 is not rotated andhence the beam is blocked by polariser 140. However, if the beam isrotated, polariser 140 will transmit at least a part of the transmittedbeam 139. The output of output 140 is then directed to CCD camera 143.Hence, CCD camera 143 is used to detect the presence of THz radiationand it also gives the spatial dependence of the reflected THz beam viathe spatial variations detected by the CCD.

FIG. 7 shows a variation on the system of FIG. 6. The system of FIG. 7is more compact than that of FIG. 6. The visible input beam 23 istransmitted onto the emitter 3 through a hole in off axis parabolicmirror 29 in the same manner as described with reference to FIG. 1. Offaxis parabolic mirror 29 is used to collect the reflected radiation anddirected into detector 33. Similarly, the transmitted radiation iscollected by off axis parabolic mirror 35 and is directed into detector39.

The main difference between this system and the system of FIG. 6 is theway in which the reference beam is combined with the reflected andtransmitted THz beams. The reference beam 27 is fed through an opticaldelay line 49 as previously described. The part of the beam 27 a whichis to be used for the reflected THz signal is passed through a firstcrossed polariser 201 a. This polarised reference beam is then passedthrough a second hole in off axis parabolic mirror 29 such that thereflected THz pass 31 and the polarised reference signal 27 a are bothdirected into the detector 33. In the same way as described withreference to FIG. 6, the THz beam 31 causes rotation of the polarisationof the reference beam 27 a. A second polariser 203 a blocks the path ofany radiation which has not been rotated. 201 a and 203 a are crossedpolarisers. The beam is then fed into CCD camera 143.

The reference beam for the transmitted beam is split off as beam 27 b.This beam is then passed through polariser 201 b to obtain a polarisedreference beam. The beam 27 b is then passed through a hole in off axisparabolic mirror 35 to combine the transmitted THz radiation 37 with thereference beam 27 b. The presence of the transmitted THz is thendetected via rotation of the polarisation of the reference beam 27 b asdescribed previously. The emergent beam is then fed into polariser 203b. Polariser 203 b is crossed with polariser 201 b such that polariser203 b blocks any radiation which has not had its polarisation vectorrotated.

FIG. 8 shows a very similar system to that of FIG. 7. Here, thoughinstead of two CCD cameras 143 and 145 a single CCD camera 151 is usedto detect both the transmitted and the reflected radiation.Specifically, the beam which is transmitted by second cross polariser203 a is directed into CCD camera 151. Also, the beam which istransmitted by second crossed polariser 203 b (transmitted radiation) isalso directed into CCD camera 151. The use of the single CCD arrayelement means that reflected and transmitted images are detectedsimultaneously.

In FIGS. 1 to 8, the sample is shown actually mounted on the emitter.This arrangement is specifically shown in FIG. 9a. To obtain a fullimage of an area of the sample, the sample is stepped relative to theTHz beam in both the x and y directions, pixel by pixel. This can bedone by mounting the sample on the emitter and moving both the emitterand the sample together using the motorised stage.

In the imaging system, both reflected and transmitted radiation must becollected. Therefore, the reflected THz pulses have to be passed backthrough the emitter crystal before reaching the off axis parabolicmirror (reference numeral 29 in FIGS. 1 to 8). In other words, theemitter acts as a window for the reflected THz. Also, to allow a largerange of sample sizes and surface curvatures to be measured, the emittermust also be sufficiently large to allow all of the reflected beams topass back through it.

FIG. 9b shows an arrangement which allows a smaller emitter to be used.In this arrangement, the sample is mounted in close proximity to theemitter (for example, between 10 and 500 μm and only the sample is movedin the x-y planes). In other words, the sample is moved relative to theemitter. To ensure high spatial resolution (i.e. in the near fieldregion), the sample must be kept close to the emitter surface. Also, thesample may be mounted on a thin window which is in turn mounted about 10to 100 μm from the surface of the emitter 3. In this case, the emitterstill needs to be large enough to permit all the reflected pulses fromthe sample to reach the off axis parabolic mirror 29. The requiredemitter size in the arrangement of 9 b is smaller than that of 9 a as in9 a, the emitter needs to be big enough to catch all reflections fromthe sample. In the arrangement in 9 b, the emitter just needs to be bigenough to catch all reflections from the small part of the sample beingimaged.

In FIG. 9c, the emitter is mounted on a THz window 4. As the mount forthe emitter transmits THz, the emitter can be made even smaller as thereis no requirement now for all of the reflected THz pulses to pass backthrough the emitter. The emitter just needs to be big enough to producethe THz beam. Again, the sample is mounted in close proximity to theemitter as opposed to onto the emitter. In this arrangement, only thesample needs to be moved. Therefore, the emitter only needs to be a fewmillimetres square in area (for example, less than 25 mm by 25 mm). Thewindow 4 is thin (between 50 μm and 300 μm) to ensure that the THz beamdiameter is still smaller than the shortest wavelength component when itreaches the sample.

FIG. 10 shows a uniform sphere 301 which will be used as a simplifiedexample for explaining the principles of the present invention. Sphere301 is formed of a dielectric material such that there is a differencein the refractive index at the THz frequencies between the sphere 301and the space in which is it located 303.

The thickness of a dielectric layer d can be deduced from the time delayτ using the relation.

τ=d(n−1)/c  (1)

where n is the index of refraction of the medium through which theradiation penetrates and c is the speed of light in free space.

Thz beam 305 is incident on sphere 301. THz beam 305 is transmittedthrough sphere 301 (shown as beam T1) and collected by transmittedradiation detector 306. The beam is also reflected from first interface307 (beam R1) and second interface 309 (beam R2). For the purpose ofthis explanation the interfaces are numbered in the order in which theyare encountered by the beam of radiation 305. The reflected THz beam iscollected by reflected radiation detector 308.

The time delay τ_(t1) of transmitted beam T1 can be used to determinethe thickness of the sample. However, it is not possible to determinewhether the object is spherical (circular) or rectangular, or any othershape, because τ_(t1) is the same for all shapes of equal thicknesses.For example, shape 311 has the same thickness as sphere 301. However,the front interface 307 of shape 301 is flat. Both sphere 301 and shape311 will give rise to the same time of flight of the transmitted signal.

To establish the shape of the object, the time delay associated with thepulse reflected R1 off first surface 307 is required. This is measuredby reflected THz detector 308. The time of flight of this pulse τ_(r1)establishes the position of the first dielectric interface (e.g.air-sphere). From this, the position of the second interface 309 can bedetermined as the thickness of the sample 301 is known from τ_(t1).

Therefore, by plotting the difference τ_(t1)−τ_(r1) at each pixelco-ordinate (x,y) relative to τ_(r1) at that pixel, one may plot out theshape of sphere 301.

The absolute position of the object may be established by plottingτ_(r1) relative to another reflection from a reference plane of knownposition, for example the top or bottom surface of a window transparentto Terahertz (not shown in FIG. 1), and placed between the incident beam305 and the sample 301 or an internal reflection in the Terahertzemitter itself (also not shown in FIG. 1).

In theory, it is possible to trace out the shapes in a similar fashionby using the time of flight τ_(r2) of the pulse R2 reflected off thesphere-air first interface 309. However, there are two reasons why thisis often not practical. Firstly, the pulse R2 is likely to be weak dueto attenuation as it travels through the sphere. This is especially truein a sample such as a human tooth, where dentine, enamel, and the cavitypulp all absorb Terahertz. Secondly, the curved nature of the sphere-airinterface 309 dictates that the reflected signal R2 is likely to falloutside the field of view of the detector. The signal R1 is closer tothe detector 308 and can be more efficiently collected. This point iseven more of a limitation in objects of arbitrary shape, where the backsurface is curved or contoured, and it is thus difficult or impossibleto judge what angle R2 is likely to be reflected through with no αpriori knowledge of the back surface 309.

The transmitted signal T1 is superior to R2 in this case because 1) thetransmitted signal is likely to be stronger than R2 because it hastraversed the sphere only once and its attenuation is therefore lessthan R2, and 2) the transmitted radiation detector 306 can be accuratelyplaced quite close to the object and hence collect all the radiation T1.

The sphere of FIG. 10 was uniform with no internal interfaces. Thesituation is more complicated where there are a plurality of internalinterfaces. FIG. 11 shows a more general case of FIG. 10, where 3Dsample 313 comprises a plurality of concentric dielectric spheres. Thesample is located in free space ‘a’. The sample has an outermost sphere‘b’, a middle sphere ‘c’ and an inner sphere ‘d’. In general, eachsphere will have a different absorption coefficient and refractiveindex.

In a manner similar to that described with reference to FIG. 10, thesample 313 is irradiated with THz radiation 305. The transmittedradiation is collected using reflected radiation detector 308.Initially, the signal collected by the reflected radiation detector willbe discussed.

To construct an image with absolute co-ordinates, a reflection from areference plane of known position is required, for example the top orbottom surface of a window transparent to Terahertz and placed betweenthe incident beam 305 and the sample 313 (not shown), or an internalreflection in the Terahertz generation crystal (not shown).

The three of the strongest signals detected by reflected radiationdetector 308 will be the reflection from the from a-b interface 315, thereflection from the b-c interface 317 and the reflection from the c-dinterface 319.

The position of the a-b interface 315 can be determined by measuring thetime delay τ_(r1) associated with pulse reflected from interface 315.Comparing τ_(r1) to time delay associated with the pulse reflected froma reference plane (not shown), the position of the interface a-b can bedetermined.

The position of the b-c interface 317 can be determined by measuring thetime delay τ_(r2) associated with pulse reflected from the interface317. By comparing this to time delay associated with the pulse reflectedfrom a-b interface 315, the position may be obtained by plotting thethickness determined from (τ_(r2)−τ_(r1))c/2n relative to the positiondetermined from τ_(r1).

In determining the position of b-c interface 317, the refractive index nof region b should be used to correct for material contributions to theτ_(r2)−τ_(r1). ‘c’ is the speed of light in free space (n=1).

The position of the c-d interface 319 can be determined by measuring thetime delay τ_(r3) associated with pulse reflected from the interface319. By comparing this to time delay associated with the pulse reflectedfrom b-c interface 317, the position can be obtained by plotting thethickness determined from (τ_(r3)−τ_(r2))c/2n relative to the positiondetermined from τ_(r2). In determining the position of interface b-c,the refractive index n of region c should be used to correct formaterial contributions to the τ_(r3)−τ_(r2). ‘c’ is the speed of lightin free space (n=1).

The position of the ‘deeper’ interfaces d-c 321, c-b 323, and b-a 325are determined using the data collected by detected transmittedradiation detector 306.

In order to use reflection and transmission data together, it isnecessary to establish a common time zero, and the plot the variousdelay times τ_(r1), τ_(r2) . . . , and τ_(t1), τ_(t2), after this timezero. Time zero can be taken as T_(ref)/2 T_(ref) is the time at whichthe reference pulse reaches the reflected radiation detector 308. Thisis essentially time at which the incident pulse 305 leaves the referenceplane and travels towards the sample 313.

The next step in constructing the 3D image is to plot the position ofthe interface d-c 321 (unknown) relative to the position c-d 319 knownfrom the reflection analysis above. This involves using the time delaybetween the beam reflected from c-d interface 319 and transmitted frominterface d-c 321.

Radiation transmitted through the sample will undergo multiplereflections before it is transmitted. The signal due the radiation whichhas not undergone multiple reflection and has just passed through thesample 313 is t1. The time of flight of t1 through the sample is τ_(t1).

Transmitted beam t2 which is detected by transmitted radiation detector306 has been transmitted through interfaces 315, 317, 319, 321 and 323.However, the beam is reflected back into the sample 313 at b-a interface325. t2 is reflected for a second time by c-b interface 323 and exitsthe sample 313 to be collected by transmitted radiation detector 306.The time of flight of beam t2 is τ_(t2).

Transmitted beam t3 which is detected by transmitted radiation detector306 has been transmitted through interfaces 315, 317, 319, 321 and 323.However, the beam is reflected back into the sample 313 at b-a interface325. t3 is transmitted through interface 321 and is reflected for asecond time by d-c interface 321 and exits the sample 313 to becollected by transmitted radiation detector 306. The time of flight ofbeam t3 is τ_(t3).

Transmitted beam t3 undergoes multiple reflections before it is detectedand therefore incurs additional delays, it is necessary to correct forthese additional delays. For the transmitted pulse 3, one wants to knowat what time t_(t3)′ the transmitted pulse first passed through theinterface d-c 321.

The time τ_(t2′) at which the pulse passed through interface c-b iscalculated from

τ_(t2)′=τ_(t1)−(τ_(t2)−τ_(t1))/2.

The time t_(t3)′ at which the pulse passed through interface d-c iscalculated from

τ_(t3)′=τ_(t2)′−(τ_(t3)−τ_(t2))/2.

The position of d-c can now be obtained by plotting the thicknessobtained from (τ_(t3)′−τ_(r3))c/n relative to the position of interfacec-d determined from τ_(t3) (see above). In determining the position ofinterface d-c, the refractive index n of region d should be used tocorrect for material contributions to the τ_(t3)′−τ_(r3)in this contextis the time at which reflected pulse 3 is reflected from the interfacec-d relative to reference time zero.

The position of c-b can be obtained by plotting the thickness obtainedfrom (τ_(t3)−τ_(t2))c/2n and adding this to position obtained fromτ_(t3)′ above. Materials contributions from the refractive index n ofregion c are also included.

The position of b-a can be obtained by plotting the thickness obtainedfrom (τ_(t2)−τ_(t1))c/2n and adding this to position obtained fromτ_(t2) above. Materials contributions from the refractive index numberof region b are also included.

FIG. 12 shows how such a system might be implemented technologically toscan a tooth.

The sample is tooth 331 which is a living tooth and is located in gum333. The tooth is imaged using THz 3D imaging system 335. The THz 3Dimaging system comprises a THz emitter/detector 337 which emits the THzradiation and also serves to detect reflected THz addition in the samemanner as that described with reference to detector 308 in FIGS. 10 and11. Radiation transmitted through the tooth 331 is detected bytransmitted THz radiation detector 339 which is used to collected theradiation in the same manner a detector 306 described with reference toFIGS. 10 and 11.

The details of the THz emitter/detector 337 and the detector 339 willnot be described here. However, an arrangement as described withreference to any of FIGS. 1 to 9 could be used. In the specific exampleshown in FIG. 12, multi element detectors are used to detect both thetransmitted and reflected radiation. This means that there is not needto scan the beam or the sample as the detectors are configured tocollect transmitted or reflected radiation from all of the requiredpixels at the same time.

The multi-element head is formed from a plurality of fibre optic cablesconfigured to collected the transmitted or reflected radiation.Information carried by the detected THz radiation may be converted intoanother form at the probe prior to transmitting away form the probe foranalysis. For example, the THz frequency may be stepped up fortransmission. Alternatively a reference beam may be supplied to thedetector and the AC Pockels effect may be used to allow rotation of thepolarisation of the reference beam in accordance with the detected THzsignal as described with reference to FIGS. 4 and 6. The reference beamwith the rotated polarisation vector can then be transmitted away fromthe probe using a polarising preserving fibre for each element pixel ofthe detector.

The detector/emitter 337 and the emitter 339 are located on probe 341.The probe is ‘Y’ shaped such that the tooth 331 is located between thearms of the Y when the probe is n position on the tooth 331. Thedetector/emitter 337 and the detector 339 sit at the end of the arms ofthe ‘Y’ on either side of the tooth 331.

A fibre optic cable 343 is connected to the top of the inverted ‘Y’ ofprobe 341. Cable 343 carries radiation to the probe 341 for imaging andalso carries information away from probe 341.

The fibre optical cable 343 is connected to laser source, delay control,beam splitter and CCD camera 345. These have been explained withreference to FIG. 6. This is in turn connected to a computer 347 fordisplaying the three dimensional image.

The actual data would be analysed in the same way as described withreference to FIG. 11. For example, in FIG. 11, the regions could bedesignated as follows: a=air, b=enamel, c-dentine, and d=pulp. Theinventors have calculated the refractive index for enamel and dentine(3.2 and 2.6, respectively) and pulp (typically 2.0) and hence are ableto use the time delay in conjunction with Equation 1 to characterize thethickness and hence position of the various dielectric layers, which inturn allows a 3D image of the tooth (sphere) to be constructed.

What is claimed is:
 1. A method of imaging a sample, the methodcomprising the steps of: (a) irradiating the sample to be imaged with anirradiating beam of pulsed electro magnetic radiation with a pluralityof frequencies in the range from 25 GHz to 100 THz, (b) simultaneouslydetecting both the radiation transmitted through the sample and theradiation reflected by the sample; (c) generating an image of the samplefrom the radiation detected in step (b).
 2. The method of claim 1,wherein step (c) comprises the step of calculating the time of flight ofa pulse transmitted through the sample; calculating the time of flightof a pulse reflected from an interface or surface of the sample; andplotting the difference or function of the difference of the time offlight of the transmitted and reflected pulse relative to the time offlight of the reflected pulse.
 3. The method of claim 1 wherein step (c)further comprises the steps of extracting the parts of the transmittedpulse which are due to an even number of reflections within the sample,and determining the position of an interface using the signal caused bysaid even number of reflections.
 4. The method of claim 1, furthercomprising the step of detecting a reference signal obtained from anobject having a known separation from either the emitter of irradiatingbeam or the sample to be imaged.
 5. The method of claim 4, wherein thereference signal is obtained from a reflection off a component of theemitter.
 6. The method of claim 1, wherein the irradiating beam has abeam diameter smaller than that of the smallest radiation wavelength ofthe beam.
 7. The method of claim 1, wherein the irradiating beam isemitted by an emitter, the emitter being irradiated with at least oneinput beam of radiation with frequencies in the visible or near infrared frequency range, the emitter being a material with non-linearoptical properties.
 8. The method of claim 4, wherein the input beam hasa beam diameter which is smaller than the smallest wavelength of thebeam of pulsed radiation of step (a).
 9. The method of claim 7, whereinthe emitter is a semiconductor.
 10. The method of claim 7, wherein thematerial with non-linear optical properties is chosen from the group ofLiIO3, NH4H2PO4, ADP, KH2PO4, KH2ASO4, Quartz, AlPO4, ZnO, CdS, GaP,GaAs, BaTiO3, LiTaO3, LiNbO3, Te, Se, ZnTe, ZnSe, Ba2NaNb5O15, AgAsS3,proustite, CdSe, CdGeAs2, AgGaSe2, AgSbS3, ZnS, DAST(4-N-methylstilbazolium) or Si.
 11. The method of claim 7, where thesample is mounted such that there are no active optical componentsbetween the sample and the emitter.
 12. The method of claim 7, whereinthe emitter is configured to hold the sample.
 13. The method of claim 7,wherein the sample is positioned with a separation from 10 mm to 500 mmfrom the emitter.
 14. The method of claim 7, wherein the emitter is of asize such that radiation reflected from the sample can pass back throughthe emitter.
 15. The method of claim 7, wherein the emitter issubstantially transparent to the irradiating beam.
 16. A methodaccording to claim 1, wherein a CCD camera is used to detect theradiation reflected from and transmitted through the sample.
 17. Themethod of claim 1, wherein a three dimensional image is generated instep (c).
 18. The method of claim 1, wherein a compositional image isgenerated in step (c).
 19. An apparatus for imaging a sample, theapparatus comprising: a) means for irradiating a sample to be imagedwith an irradiating beam of pulsed electromagnetic radiation with aplurality of frequencies in the range from 25 GHz to 100 THz; b) meansfor detecting radiation which is both transmitted through and reflectedfrom the sample; and c) means for generating an image of the sample fromradiation detected in step (b).
 20. The apparatus of claim 19, whereinthe means for generating an image comprise means for calculating thetime of flight of a pulse of radiation transmitted through the sample,means for calculating the time of flight of a pulse of radiationreflected from an interface or surface of the sample; and means forplotting the difference or a function of the difference in the time offlight of the transmitted and reflected pulse relative to the time offlight of the reflected pulse.
 21. The apparatus of claim 19, whereinthe means for generating an image of the sample comprise means forextracting the parts of the transmitted pulse which are due to an evennumber of reflections within the sample, and determining the position ofan interface using the signal caused by said even number of reflections.22. The apparatus of claim 19, further comprising means for generating areference signal.
 23. The apparatus of claim 22, wherein the means forgenerating a reference signal comprise means for measuring a signalreflected from a component of the means for irradiating the sample. 24.The apparatus of claim 19, wherein the means for irradiating a sample,comprises an emitter for emitting the irradiating beam, the emitterhaving optical non-linear properties, such that when the emitter isirradiated with an input beam with a frequency in the visible or nearinfra-red frequency ranges, a beam is emitted with frequencies in therange from 25 GHz to 100 THz.
 25. An apparatus according to claim 23,wherein the input beam of pulsed radiation has a diameter which issmaller than that of the smallest wavelength of the irradiating beam.26. The apparatus of claim 19, wherein the means for detecting theradiation comprises a CCD camera for detecting the reflected radiation.27. The apparatus of claim 19, wherein the means for generating an imageof the sample comprises means for generating a three dimensional imageof the sample.
 28. The apparatus of claim 19, wherein the means forgenerating an image of the sample comprising means for generating acompositional image of the sample.